Special Points of Inflation in Flux Compactifications

TL;DR

This work addresses the challenge of realizing large-field axion inflation within string theory by exploiting axions that live in the complex structure moduli spaces of Calabi–Yau manifolds. The authors develop a monodromy-based framework, identifying special points with infinite-order monodromies where the Kähler potential has an approximate shift symmetry and deriving flux-induced superpotentials that generate inflaton potentials. They analyze one-parameter Calabi–Yau threefolds and elliptic fibrations, obtaining a spectrum of inflationary potentials, including polynomial, cosine-type, and Mordell–Weil–inspired forms, and extend the discussion to F-theory on CY4s to incorporate seven-brane moduli. The results provide a structured way to assemble axion inflation models from intrinsic geometric data, while highlighting the stabilization challenges and the need for careful handling of moduli mixing in realistic constructions. Overall, the paper maps concrete geometric loci to inflationary dynamics, offering a principled route to embed axion inflation in string theory and guiding future explorations of moduli stabilization and phenomenology.

Abstract

We study the realisation of axion inflation models in the complex structure moduli spaces of Calabi-Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell-Weil group of rank $N-1$ or an $N$-section, which admit an axion if $N>3$.

Figures (3)

• Figure 1: Schematic depiction of singular points in complex structure moduli space with infinite-order monodromy $z_1$ and finite-order monodromy $z_2$. An axions can be identified very close to the point $z_1$.
• Figure 2: Schematic depiction of the one-parameter moduli space of Calabi-Yau threefolds with three special points. $M_0$, $M_1$, and $M_\infty$ denote the monodromy matrices around these points.
• Figure 3: Schematic depiction of the $s$-plane including two contours, dotted green line and solid green line. The crosses indicate poles at $s = -\alpha_i - n$ with $n=\{0,1,2,\ldots \}$, while the small spheres indicate poles at $s=\{0,1,2,\ldots \}$.